A Deterministic Framework for Neural Network Quantum States in Quantum Chemistry

We present a deterministic optimization framework for neural network quantum states (NQS) designed to bypass the sampling variance and slow mixing issues inherent in stochastic optimization. By projecting a neural backflow ansatz onto dynamically evolving configuration subspaces, our method provides a systematic route for optimizing the selected variational component of the wave function and estimating residual correlation through a posthoc second-order perturbative correction. The implementation utilizes a hybrid CPU-GPU architecture that shows empirical sublinear wall-time scaling with respect to the subspace size over the tested range, enabling the calculation of strongly correlated systems, such as the chromium dimer, within Hilbert spaces of 10²³ configurations. Benchmarks on molecular bond dissociations demonstrate that this deterministic approach yields stable convergence and accuracies comparable to selected reference methods in the tested systems.